Regarding the hardware -- lack of HDMI and the problems with bluetooth certainly limit the utility of Linux on the tablet.
Are the bluetooth problems related to Google's throwing out bluez in favour of an inadequately tested Broadcom thing for Jelly Bean 4.2? If so, rolling back to bluez would seem the way to go.
What I would like from a tablet is the ability to run android AND a linux environment. So a chroot works nicely for me. It's a laptop when I want it to be one, and a tablet (including kindle app, Angry Birds, and whatnot) when I want it to be one.
Microsoft of all people seems to have figured out that many people would want a tablet that is usable as a laptop. I dearly hope that the Surface or Surface Pro (a) succeed and (b) can run linux eventually. Some new/upcoming models from Lenovo, Samsung and others also look promising.
I'm even seriously considering a Surface Pro with Windows 8, and putting cygwin on it! It may be good enough for my mobile needs. It depends on the price, however.